I can interpret functions in the formula form but I simply can’t understand how it can become a graph. How would you transform one into the other?
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A function will usually be expressed as an equation that sets a variable, _y_, to some expression including another variable _x_.
On a graph, _x_ is the _independent variable_. It’s the one whose value you get to change just because you want to.
The other variable, _y_, is the _dependent variable_. You don’t set that one directly, you can only find out what it is by setting _x_ to a value and solving the expression.
On a graph, _x_ goes on the horizontal axis. When you pick a value of _x_ and solve it, put a dot for _y_ at the right distance above or below the horizontal axis for that value of _x_. If the function is _y = x_, and you pick 2 for _x_, you put a dot 2 units above the x axis at 2 units to the right of where the horizontal and vertical axes cross.
If you do that for all possible values of _x_, you will get a shape on your graph. For _y = x_, it’s a straight line ascending at 45° right through the origin (where the axes cross).
Part of the definition of a function is that every value of _x_ gives you exactly one unique value for _y_, so you will never see a line double back above the horizontal axis, it only moves up & down across all values of _x_.
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